Have you listened to your phone? If you lift the handset and just listen, you may be able to hear some background noise or crackling. If that's the case, you need to have a chat with you BT fault line and let them know there's a line problem.
We lost our BB connection over Christmas last year! Nice lady down hole in street managed to reconnect a dodgy bit of wire on the 28th Dec. Kids were none too happy about that. Not to mention that the first bloke who tried to sort it managed to completely stuff the landline on Christmas Eve - and guess what, the spares department is shut over Christmas!
The other thing to try is to switch off your modem, leave it for about ten seconds and switch it back on. Sometimes they get a bit "confused" and rebooting sorts them out. Modern ones are less likely to suffer from "confusion" though as they are quite good at self-healing.
Other than that. You might try a complete virus check, with new virus definitions, same for the spyware stuff. It may be that you've got a "lodger" on your PC that's hogging bandwidth. There are a couple of sneaky ones that don't use the connection until you've got traffic running on it and therefore you don't see any activity when you're idle.
Do you use IE6 or Firefox (or any other browser for that matter)? If you have a couple of browsers available, try using one that you don't normally run and see if that makes a difference when you do speed checks.
Final thing might be to try a repair of your Windows (assumption) system.
If none of that lot works, or at least helps narrow down the problem, I'm sure one of the REAL gurus will be able to point you in a few other directions.
Good hunting
ST